提出加权样本协方差的渐近非线性收缩公式，提升估计精度。
Asymptotic non-linear shrinkage and eigenvector overlap for weighted sample covariance
- 基于加权样本协方差推导渐近非线性收缩公式
- 公式适用于指数加权情形，数值算法可高效计算
- 在重尾分布下仍保持稳健，适合金融与高维数据
我们计算了加权样本协方差的协方差矩阵和精度矩阵估计器的渐近非线性收缩公式，以及样本与总体特征向量重叠的联合分布，延续Ledoit和Péché的研究思路。特别详细推导了指数加权样本协方差的情形，并提出一种数值计算这些公式的算法。实验验证了渐近非线性收缩估计器的性能表现。最后，测试了该理论对重尾分布的鲁棒性。
原文摘要 · Abstract (English)
We compute asymptotic non-linear shrinkage formulas for covariance and precision matrix estimators for weighted sample covariances, and the joint sample-population eigenvector overlap distribution, in the spirit of Ledoit and Péché. We detail explicitly the formulas for exponentially-weighted sample covariances. We propose an algorithm to numerically compute those formulas. Experimentally, we show the performance of the asymptotic non-linear shrinkage estimators. Finally, we test the robustness of the theory to a heavy-tailed distributions.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。